Solve sqrt{0.64}-sqrt{21/4}+sqrt{144}

$$\sqrt { 0.64 } - \sqrt { 2 \frac { 1 } { 4 } } + \sqrt { 144 }$$

Evaluate

$$11.3$$

Solution Steps

Calculate the square root of 0.64 and get 0.8.

$$0.8-\sqrt{\frac{2\times 4+1}{4}}+\sqrt{144}$$

Multiply 2 and 4 to get 8.

$$0.8-\sqrt{\frac{8+1}{4}}+\sqrt{144}$$

Add 8 and 1 to get 9.

$$0.8-\sqrt{\frac{9}{4}}+\sqrt{144}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$0.8-\frac{3}{2}+\sqrt{144}$$

Convert decimal number 0.8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}-\frac{3}{2}+\sqrt{144}$$

Least common multiple of 5 and 2 is 10. Convert \frac{4}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{8}{10}-\frac{15}{10}+\sqrt{144}$$

Since \frac{8}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-15}{10}+\sqrt{144}$$

Subtract 15 from 8 to get -7.

$$-\frac{7}{10}+\sqrt{144}$$

Calculate the square root of 144 and get 12.

$$-\frac{7}{10}+12$$

Convert 12 to fraction \frac{120}{10}.

$$-\frac{7}{10}+\frac{120}{10}$$

Since -\frac{7}{10} and \frac{120}{10} have the same denominator, add them by adding their numerators.

$$\frac{-7+120}{10}$$

Add -7 and 120 to get 113.

$$\frac{113}{10}$$

Factor

$$\frac{113}{2 \cdot 5} = 11\frac{3}{10} = 11.3$$